A particle is projected with an angle of projection $\theta$ to the horizontal line passing through the points $( P , Q )$ and $( Q , P )$ referred to horizontal and vertical axes (can be treated as $x$-axis and $y$-axis respectively).
The angle of projection can be given by
A particle is projected with an angle of projection $\theta$ to the horizontal line passing through the points $( P , Q )$ and $( Q , P )$ referred to horizontal and vertical axes (can be treated as $x$-axis and $y$-axis respectively).
The angle of projection can be given by
- [AIIMS 2015]
- A
$\tan ^{-1}\left[\frac{ P ^2+ PQ + Q ^2}{ PQ }\right]$
- B
$\tan ^{-1}\left[\frac{ P ^2+ Q ^2- PQ }{ PQ }\right]$
- C
$\tan ^{-1}\left[\frac{ P ^2+ Q ^2}{2 PQ }\right]$
- D
$\sin ^{-1}\left[\frac{ P ^2+ Q ^2+ PQ }{2 PQ }\right]$
Similar Questions
The angle of projection at which the horizontal range and maximum height of projectile are equal is
The angle of projection at which the horizontal range and maximum height of projectile are equal is
If T is the total time of flight, $h$ is the maximum height $ \& R$ is the range for horizontal motion, the $x$ and $y$ co-ordinates of projectile motion and time $t$ are related as
If T is the total time of flight, $h$ is the maximum height $ \& R$ is the range for horizontal motion, the $x$ and $y$ co-ordinates of projectile motion and time $t$ are related as
Column $-I$
Angle of projection
Column $-II$
$A.$ $\theta \, = \,{45^o}$
$1.$ $\frac{{{K_h}}}{{{K_i}}} = \frac{1}{4}$
$B.$ $\theta \, = \,{60^o}$
$2.$ $\frac{{g{T^2}}}{R} = 8$
$C.$ $\theta \, = \,{30^o}$
$3.$ $\frac{R}{H} = 4\sqrt 3 $
$D.$ $\theta \, = \,{\tan ^{ - 1}}\,4$
$4.$ $\frac{R}{H} = 4$
$K_i :$ initial kinetic energy
$K_h :$ kinetic energy at the highest point
|
Column $-I$ Angle of projection |
Column $-II$ |
| $A.$ $\theta \, = \,{45^o}$ | $1.$ $\frac{{{K_h}}}{{{K_i}}} = \frac{1}{4}$ |
| $B.$ $\theta \, = \,{60^o}$ | $2.$ $\frac{{g{T^2}}}{R} = 8$ |
| $C.$ $\theta \, = \,{30^o}$ | $3.$ $\frac{R}{H} = 4\sqrt 3 $ |
| $D.$ $\theta \, = \,{\tan ^{ - 1}}\,4$ | $4.$ $\frac{R}{H} = 4$ |
$K_i :$ initial kinetic energy
$K_h :$ kinetic energy at the highest point
A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is
A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is
- [AIIMS 1998]
Aball is thrown from a point on ground at some angle of projection. At the same time a bird starts from a point directly above this point of projection at a height $h$ horizontally with speed $u$. Given that in its flight ball just touches the bird at one point. Find the distance on ground where ball strikes
Aball is thrown from a point on ground at some angle of projection. At the same time a bird starts from a point directly above this point of projection at a height $h$ horizontally with speed $u$. Given that in its flight ball just touches the bird at one point. Find the distance on ground where ball strikes